The presidents of Ukraine and Russia said the ceasefire between Ukrainian forces and Russian-backed rebels was mostly holding, but the truce still appeared fragile in its first full day as both sides of the conflict claimed violations.

A statement from Ukrainian president Petro Poroshenko's office said he and Russian president Vladimir Putin discussed steps "for giving the ceasefire a stable character" in a telephone conversation on Saturday.

But, it said, both leaders assessed the ceasefire as having been "fulfilled as a whole." A separate Kremlin statement about the call said: "There was a mutual satisfaction with the fact that the sides of the conflict were overall observing the ceasefire regime."

Andriy Lysenko, a spokesman for Ukraine's national security council, told reporters that rebels had fired at Ukrainian forces on 10 occasions on Friday night after the ceasefire was to take effect.

In Donetsk, the largest city controlled by the Russian-backed separatists, the night passed quietly - a rarity after several months of daily shelling in residential areas. But Alexander Zakharchenko, the top separatist leader from Donetsk, told the Russian news agency RIA Novosti that the ceasefire had been violated with two rounds of shelling in the town of Amvrosiivka, about 30 miles south east of Donetsk.

Mr Lysenko said Ukrainian forces were strictly observing the ceasefire.

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Earlier on Saturday, the mayor's office in Donetsk said there had been no reports of shooting or shelling there, although some shelling had been heard late on Friday afternoon. The city council of the second-largest rebel-held city of Luhansk, which had endured intense fighting for weeks, also reported the night was quiet.

Along the coast of the Sea of Azov, where rebels allegedly backed by Russian troops opened a new front two weeks ago, government and separatist forces were keeping a distance of about 12 miles between them, according reports. The remains of a Ukrainian tank smashed by rocket fire lay along the road, evidence of the fighting that raged until just before the ceasefire.

Ukraine, Russia and the Kremlin-backed separatists signed the cease-fire deal on Friday in Minsk, the Belarusian capital, in an effort to end more than four months of fighting in the region. The negotiators also agreed on the withdrawal of all heavy weaponry, the release of all prisoners and the delivery of humanitarian aid to devastated cities in eastern Ukraine.

If the ceasefire holds, it would be a landmark achievement for both sides. Fighting between pro-Russian rebels and Ukrainian government troops has ravaged the Ukrainian economy, claimed at least 2,600 civilian lives and left hundreds of thousands homeless, according to United Nations estimates.

US president Barack Obama said he was hopeful the ceasefire would hold.

"It has to be tested," Mr Obama said on Friday at the closing of a two-day Nato summit in Wales.

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Both the US and the European Union have prepared even tougher sanctions on Moscow, and Mr Obama stressed that the most effective way to ensure the ceasefire's success was to move ahead with those measures and maintain pressure on Russia.

According to an EU diplomat, these new measures would target Russia's access to capital markets and trade in arms and defence technology, dual-use goods and sensitive technologies. The new sanctions were given preliminary approval on Friday night and could be implemented as early as Tuesday.

"If certain processes get under way, we are prepared to suspend sanctions" against Russia, German Chancellor Angela Merkel said.

In a statement published online on Saturday, Russia's foreign ministry condemned further EU sanctions and promised that "there will undoubtedly be a reaction from our side" to any new measures.